One-sided Cauchy-Stieltjes kernel families

DOI10.1007/S10959-010-0303-XzbMath1219.60012arXiv0906.4073OpenAlexW3098442735MaRDI QIDQ548159

Abdelhamid Hassairi, Wlodzimierz Bryc

Publication date: 28 June 2011

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.4073

zbMATH Keywords

exponential familiesCauchy kernelfree stable law

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Free probability and free operator algebras (46L54)

Related Items (11)

A survey on the effects of free and Boolean convolutions on Cauchy-Stieltjes kernel families ⋮ On Cauchy-Stieltjes kernel families ⋮ Characterization of quadratic Cauchy-Stieltjes kernel families based on the orthogonality of polynomials ⋮ The mean of the reciprocal in a Cauchy-Stieltjes family ⋮ On polynomials associated with Cauchy–Stieltjes kernel families ⋮ Explicit free multiplicative law of large numbers ⋮ Cauchy–Stieltjes families with polynomial variance functions and generalized orthogonality ⋮ BOOLEAN MULTIPLICATIVE CONVOLUTION AND CAUCHY-STIELTJES KERNEL FAMILIES ⋮ Variance function of Boolean additive convolution ⋮ On some properties of Cauchy-Stieltjes kernel families ⋮ A characterization of the Marchenko-Pastur probability measure

Cites Work

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• Natural real exponential families with cubic variance functions
• Gibbs sampling, exponential families and orthogonal polynomials
• Free generalized gamma convolutions
• Addition of freely independent random variables
• Stable laws and domains of attraction in free probability theory
• Free martingale polynomials.
• FREE EXPONENTIAL FAMILIES AS KERNEL FAMILIES

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